Problem 8: Calculate the ratio of K.E and P.E of an electron in an orbit?

Solution:

K.E. = Ze2/2r

P.E. = -Ze2/r

∴ P.E. = –2K.E

∴ K.E/P.E = - 1/2

Problem 9: How many spectral lines are emitted by atomic hydrogen excited to nth energy level?

Solution:

Thus the number of lines emitted from nth energy level

= 1 + 2 + 3 +………… n – 1 = ∑(n – 1)

∑n = n(n+1)/2

∴ ∑ (n – 1) = ( n-1) (n-1+1)/2 = (n-1) (n)/2

Number of spectral lines that appear in hydrogen spectrum when an electron jumps from nth energy level = n (n-1)/2

Problem 10: Calculate (a) the de Broglie wavelength of an electron moving with a velocity of 5.0x 105 ms–1 and (b) relative de Broglie wavelength of an atom of hydrogen and atom of oxygen moving with the same velocity (h = 6.63 x 10–34 kg m2 s–1)

Solution:

(a λ = h/mv = 6.63 x 10-34 kgm2s-2/ (9.11 x 10-31kg) ( 5.0 x 105ms-1)

Wavelength λ = 1.46 x10–9m

(b) An atom of oxygen has approximately 16 times the mass of an atom of hydrogen. In the formula λ = h/mv, h is constant while the conditions of problem make v, also constant. This means that λ and m are variables and λ varies inversely with m. Therefore, λ for the hydrogen atom would be 16 times greater than λ for oxygen atom.

Problem 11: A 1 MeV proton is sent against a gold leaf (Z = 79). Calculate the distance of closest approach for head on collision.

Problem 13: The energy of electron in the second and third Bohr orbit of the hydrogen atom is –5.42 x 10–12 erg and –2.41 x 10–12erg, respectively. Calculate the wavelengths of emitted radiation when the electron drops from third to second orbit.

Problem 14: O2 undergoes photochemical dissociation into one normal oxygen and one excited oxygen atom, 1.967 eV more energetic than normal. The dissociation of O2 into two normal atoms of oxygen atoms requires 498kJ mole–1. What is the maximum wavelength effective for photochemical dissociation of O2?